1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
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15 include "ground_2/steps/rtc_shift.ma".
16 include "ground_2/steps/rtc_ist.ma".
18 (* RT-TRANSITION COUNTER ****************************************************)
20 (* Properties with test for t-transition counter ****************************)
22 lemma ist_zero_shift: āc. šā¦0,cā¦ ā šā¦0,ā*cā¦.
26 (* Inversion properties with test for t-transition counter ******************)
28 lemma ist_inv_shift: ān,c. šā¦n,ā*cā¦ ā ā§ā§ šā¦0,cā¦ & 0 = n.
30 elim (shift_inv_dx ā¦ H) -H #rt0 #rs0 #ti0 #ts0 #H1 #_ #H2 #H3 #H4 destruct
31 elim (max_inv_O3 ā¦ H1) -H1 #H11 #H12 destruct
32 elim (max_inv_O3 ā¦ H2) -H2 #H21 #H22 destruct
36 lemma ist_inv_zero_shift: āc. šā¦0,ā*cā¦ ā šā¦0,cā¦.
37 #c #H elim (ist_inv_shift ā¦ H) -H //